Comparison of Two Procedures for Predicting Rocket Engine Nozzle Performance

NASA Technical Memorandum 89814 0-' AIAA-87-207 1 I'

t Comparison of Two Procedures for Predicting Rocket Engine Nozzle Performance

Kenneth J. Davidian Lewis Research Center Cleveland, Ohio

Prepared for the 23rd Joint Propulsion Conference cosponsored by the AIAA, SAE, ASME, and ASEE San Diego, California, June 29-July 2, 1987 COMPARISON OF TWO PROCEDURES FOR PREDICTING

ROCKET ENGINE NOZZLE PERFORMANCE

Kenneth J. Davidian National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135

Abstract layer prediction proqram used in this procedure. Unlike BLIMP, BLM is accompanied by a set of sub- Two nozzle performance prediction procedures programs which will calculate all the necessary whicn are based on the standardized JANNAF meth- preliminary information required for the boundary odology are presented and compared for four layer analysis. This total set of subprograms rocket engine nozzles. The first procedure (includinq BLM) is referred to as the 1985 ver- required operator intercedance to transfer data sion of the Two-Dimensional Kinetics program between the individual performance programs. The (TDK.85) .4 second procedure is more automated in that all necessary programs are collected into a single Performance comparisons were made for noz- computer code, thereby eliminating the need for zles having area ratios 60:1, 200:1, 400:1, and data reformatting. Results from both procedures 1OOO:l. Each nozzle had a throat diameter of co Lo show similar trends but quantitative differences. 1 in. and was specified to run at a chamber pres- d P) Agreement was best in the predictions of specific sure of 1000 psia using hydrogen and oxygen as I W impulse and local skin friction coefficient. the propellants. Variations of the wall temper- Other compared quantities include characteristic ature profile were made to investigate its effect velocity, thrust coefficient, thrust decrement, on the engine performance. boundary layer displacement thickness, momentum thickness, and heat loss rate to the wall. Description of Procedures Effects of wall temperature profile used as an input to the programs was investigated by running The first procedure for evaluating the three wall temperature profiles. It was found rocket engine nozzle performance is referred to that this change greatly affected the boundary as the disjoint procedure. The succession of layer displacement thickness and heat loss to the programs used in this procedure is the One- wall. The other quantities, however, were not Dimensional Equilibrium (ODE) program,5 the drastically affected by the wall temperature pro- One-Dimensional Kinetics (ODK) program,6 and the file change. Boundary Layer Integral Matrix Procedure program ( BLIMP).2 ODE is a thermochemical Droperties Introduction program which provided throat chemical composition input data for the DDK proqram. ODK, a Accurate predictions of boundary layer kinetics program which computes finite rate reac- growth are necessary for accurate predictions in tion performance, was run from the nozzle throat rocket engine performance. Equilibrium and chem- to the exit. The results provide BLIMP with pres- ical kinetics programs already exist which pre- sure profile and chemistry information as input. dict performance losses with sufficient accuracy. The exclusion of a two-dimensional kinetics anal- However, the computer modeling of boundary layer ysis results from the fact that the 1973 version growth and its effect on rocket engine perform- of the Two-Dimensional Kinetics program (TDK.73) ance is less standardized. This is due to dif- was to be used, but it gave unstable results. ferences in the physical modeling and numerical Therefore, an average value for the equivalent procedures used. Boundary layer losses start to two-dimensional divergence efficiency of 0.996 detract greatly from the overall performance in was assumed in lieu of running TDK.73. This rocket engine nozzle designs with large exit-area divergence efficiency s equivalent to a 7.25' to throat-area ratios. These high area ratio divergence half-ang1e.j The flow diagram for nozzles (>400) are of interest for orbital trans- this procedure is shown in Fig. 1. Table 1 shows fer vehicles to obtain maximum performance as the required inputs for each program used in the indicated by high specific impulse. disjoint procedure and from which program (if any) they are generated. The purpose of this paper is to compare the results from two procedures for evaluating the The second procedure used is called the inte- performance of nozzle contours. Both procedures grated procedure. In this study, the integrated are based on the standardized JANNAF methodology1 procedure refers to a single program, the 1985 for predicting rocket engine nozzle performance. version of the TDK program (TDK.85). TDK.85 com- The first, the disjoint procedure, requires bines TDK.73 as a subproqram along with the transmission of data between three separate boundary layer module (BLM), ODE, ODK, and many performance prediction programs. The boundary other subprograms into one large program. The layer 8rediction program in this procedure is inputs required for the integrated procedure are BLIMP. BLIMP is an independent, stand-alone shown in Table 2. program and can only be utilized after prior runs of other performance programs. In this case, two Description of Programs programs were run as an input to BLIMP. The second, the integrated procedure, utilizes one The individual programs described below are performance program which ha many subroutines to performance prediction codes. perform the prediction. BLM 3 was the boundary

1 One-Dimensional Equilibrium Program (ODE)5 the kinetics variances in the nozzle downstream of the throat, and predicting the boundary layer This program calculates the equilibrium con- growth and losses. Also, the program can dis- ditions for a reactive mixture in an idealized place a potential wall contour hy the displace- closed combustion system. Reaction rates are ment thickness calculated by BLM and recompute considered to be infinitely fast so that all reac- the kinetic variances in the nozzle to attain a tions reach local equilibrium conditions. A better estimate of the boundary layer thickness. rocket performance option is run which predicts the theoretical maximum performance of isentropic Description of Input Cases convergent-subsonic and divergent-supersonic flow in a nozzle with shifting equilibrium chemical Four nozzles, with area ratios of 60:1, composition during expansion. The results from 200:1, 400:1, and 1000:1, were chosen for this ODE were used as throat condition inputs to the evaluation study. All four had 0.5 in. throat ODK program in the disjoint procedure. raiii and lengths corresponding to a 100 percent 15 cone with the same throat radius and area One-Dimensional Kinetics Program ( ODK)6 ratio.’l They all operated at 1000 psia chamber pressure and used normal boiling point (NBP) liq- This program calculates the deviation from uid hydrogen and NBP liquid oxygen as their fuel equilibrium performance in the nozzle due to and oxidizer. The propellants were injected with finite reaction rates not allowing chemical equi- a mixture ratio (O/F) of six. librium to be reached. Unlike ODE, ODK bases the fraction of mixture which will react on the reac- For the given area ratios, the nozzle exit tion rates of the mixture. ODK considers complex, radii were determined. These exit plane lengths homogeneous, ideal gas reactions in combustion and radii values are tabulated in Table 4. Since and nozzle expansion situations. Eighteen chemi- the purpose of this study was comparative in cal reactions and four three-body recombination- nature, the actual contour of the nozzles was not dissociation reactions were used by ODK for the important so long as they were the same for both fuelloxygen combination of hydrogen and oxygen procedures. The contour for each nozzle between (Table 3). The output from this program provides the throat and exit plane was calculated using an axial pressure profile along a streamline the RAO method, a method of characteristics rou- boundary (i.e. the nozzle wall) as an input to tine coupled with an optimization scheme based on the BLIMP program in the disjoint procedure. ODK the calculus of variations.8 These contours also outputs performance results including speci- (Appendix A) defined the potential flow bound- fic impulse, thrust coefficient (CF), and char- aries for each nozzle. acteristic velocity (c*). The remaininq operating conditions of the Boundary Layer Integral Matrix Procedure Program engine were used as inputs for ODK, BLIMP, and (BLIMP) TDK. The energy level associated with the oxygen is -2948 callmole and -1977 callmole for the This program calculates the boundary 1 ayer hydrogen. The geometry variables of the combus- growth in a rocket nozzle. For axisymmetric tion chamber, throat, and nozzle are shown in flow, the program can calculate either shifting Fig. 2 and the corresponding values are specified equilibrium or frozen compositions for any fuel/ in Table 5. oxidizer combination. The program uses an integral matrix solution algorithm which is equivalent For both evaluation procedures, the poten- to a higher order finite difference approach. tial wall contour was defined by specifying axial This program will output various boundary layer location values and radii at equal intervals properties as well as the coordinates of the along the nnzzle centerline. In the integrated potential flowfield if the input described the procedure, the number of contour points was real wall, or the coordinates of the.real wall if greatly reduced at the higher area ratios (>200:1) the potential flow contour was input. to insure that the contour interpolating routine would not compute an erratic wall slope between Two-Dimensional Kinetics Program 1983 Version input wall points. The number of points given ITDK. 83)j for each area ratio for both procedures, the number of points on the sonic line at the throat This program is really a combination of pro- (required to set-up the method of characteristics grams. It incorporates the ODE and ODK programs mesh), and the number of segments used in the along with a transsonic module (TRANS), a method boundary layer prediction (for the integrated of characteristics routine (MOC), a two- procedure) is shown in Table 6. dimensional kinetics effects module, and a boundary layer predictor (ELM). TDK.83 integrates all Each nozzle had the same baseline wall tem- the pieces which were used in the disjoint proce- perature profile. The wall temperature profile dure and passes the needed information between of the 1OOO:l nozzle is shown in Fig. 3. The the programs automatically. The results of each smaller area ratio nozzles used this same profile run are printed out in a summary table at the end truncated at the axial position of the nozzle of a run. The program provides the user with the exit. The profile for all four nozzles assumed a capability of using specific combinations of sub- cooled throat section, and a radiation cooled routines for each section of the engine. All the nozzle. Near the throat, the profile used is computations involved with analyzing a rocket very similar to that calcul ted for the Space engine nozzle are achieved with one computer run. Shuttle Main Engine (SSME).’ It is much cooler This includes evaluation of the kinetic devia- in the throat region than the calcul ated tempera- tions from equilibrium performance, calculation ture for the RL1$ due to the difference in of the sonic line in the throat region, setting materials of construction. Figure 4 shows the up the mesh of characteristic lines, calculating wall temperature profiles of the 200:l nozzle,

2 the RL10, and the SSME superimposed on the same More subtle differences are found in the plot for comparison purposes. eddy-viscosity models used by the two boundary layer programs. These also directly affect the Discussion of Results prediction of the boundary layer profiles. BLIMP uses the original Ceheci-Smith eddy-viscosity The results of the computer runs showed sim- model whereas BLM uses a revised version of the ilar trends for all the area ratios considered. same model. For example, BLM uses kinematic vis- The general discussion of results will cover all cosity, intermittancy, and transitional terms in the nozzles investigated, however, only figures the near-wall region expression of the dimension- for the 1OOO:l case will be shown since they are less eddy-viscosity whereas BLIMP does not. characteristic of all the results. The 1OOO:l area ratio is also of particular interest for an -Local Skin Friction Coefficient orbital transfer vehicle. The quantities which are compared include the boundary layer displace- Figure 7 shows the local skin friction coef- ment thickness, momentum thickness, local skin ficient for the 1OOO:l nozzle. The local skin friction coefficient, thrust loss, heat loss to friction coefficient is defined as the ratio of the wall , the characteristic velocity (c*), thrust shear stress at the wall to the local dynamic coefficient (CF), and specific impulse (Isp). pressure. The closest agreement at the exit plane (a difference of 1.5 percent) occurs in the 1OOO:l Boundary Layer Displacement and Momentum Thickness area ratio case and the larqest difference (10.2 percent) occurs at the 400:l area ratio. Figure 5 is a comparison between the boundary layer displacement thickness as calculated by Thrust Decrement Due to Boundary Layer Growth the disjoint procedure and the integrated procedure for the 1OOO:l nozzle. The boundary layer The thrust decrement is the loss of thrust dispiacement thickness predictions for the two due to skin friction ettects on the boundary layer procedures agree near the throat but then diverge displacement thickness and the wall pressure pro- monotonically toward the exit plane. Agreement file in the nozzle. Figure 8 shows the predic- between the two code's exit plane predictions is tion comparisons of thrust decrement for the very good for the 60:l area ratio case (only a 1OOO:l case. In all four area ratio cases the 1.4 percent difference). However, the 200:1, prediction at the throat by the disjoint proce- 400:1, and 1OOO:l cases show a 10.5, 39.6, and dure is qreater than that of the integrated pro- 35.8 percent difference between the exit plane cedure. The integrated procedure diverges from values for the two procedures, respectively. The the disjoint procedure solution downstream of the disjoint procedure predicts a greater displace- throat and predicts a greater value at the exit ment thickness value and rate of growth than does plane, as is shown in the figure. The thrust the integrated procedure. These differences decrement predictions vary by 12.5, 20.3, 22.3, between the two procedures in boundary layer dis- and 32.2 percent for the 60:1, 200:1, 400:l and placement thickness are good examples of the rea- 1OOO:l nozzles, respectively. son for this study. Since the thrust decrement can be directly Figure 6 shows a comparison of the momentum related to the size of the boundary layer, the thickness profiles in the axial direction as pre- reasons for the discrepancies between the two dicted by the disjoint procedure and the integra- procedures are similar to those described in the ted procedure for the 1OOO:l area ratio nozzle. displacement thickness section. The integrated procedure predicts a nearly linear increase in momentum thickness from the throat to Heat Loss to the Wall the exit, while the disjoint procedure shows a gently concave profile which is always greater The heat loss to the wall profiles are than the integrated procedure profile. This derived from the integration of the amount of results in a slightly higher prediction by the heat being directed at the nozzle wall per unit disjoint procedure at the exit plane for every area per unit time. By integrating this quantity case. Differences between the two procedures' locally over the entire nozzle length, the result momentum thickness predictions are 11.6, 11.3, is a cumulative heating rate, with units of 18.4, and 16.2 percent for the 60:1, 200:1, BTU/sec. The value of heat loss to the wall is 400:1, and 1OOO:l area ratio cases respectively. primarily dependent on the wall temperature profile and the heat transfer coefficient. Integra- A possible reason for the discrepancies tion is performed by the computer programs. The between the two procedures is that the wall comparison of the profiles of the total heat loss pressure profile resulting from the disjoint pro- rate to the wall are characterized by the 1000:1 cedure was different than that used in the inte- area ratio case, as shown in Fig. 9. The values grated procedure. In the disjoint procedure, the predicted by the disjoint procedure are plotted wall pressure profile was output from the ODK starting from the throat whereas the integrated program and used as an input to the BLIMP program. procedure's values begin approximately 20 percent In the integrated procedure, the wall pressures of the nozzle length downstream of the throat. were calculated internally by the TDK subprogram. This is because the integrated procedure divides TDK will generally predict larger values of wall the nozzle into segments and gives an integrated pressure than will ODK. The differences between heat flux value at the end of each segment. The these values for similar axial stations were as values predicted by both procedures at this point large as a factor of two. This large discrepancy show good agreement in the throat region. How- can change the fluid properties at the edge of ever, as the analysis travels down the nozzle the boundary layer drastically. This, in turn, toward the exit plane, the predicted values affects the boundary layer profiles as seen in diverge rapidly. The difference between predic- the displacement or momentum thickness plots. ted values at the exit plane are 14.9, 20.0, 22.7,

3 and 26.8 percent for the 60:1, 200:1, 400:1, and The absolute specific imDulse values calcu- 1OOO:l nozzles respectively. In all cases, the lated by both procedures ar? all very close, as integrated procedure predicts a greater value of shown in Fiq. 10. The uredictions differ by 0.10, heat loss to the wall for the same wall tempera- 0.51, 0.64, and 1.30 percent for the 60:1, 200:1, ture profile. The difference is probably due to 400:1, and the 1OOO:l case, respectively. In all the difference in wall pressure profiles used in cases, the disjoint procedure predicts an Is, the two procedures as well as a difference in the value higher than those of the integrated proce- surface coefficients of heat transfer. dure. The specific impulse calculated by the ODE portion of hoth procedures is within 0.25 percent Characteristic Velocity, c* due to thermodynamic database differences mentioned Dreviously. The inteqrated procedure con- Analytically, the characteristic velocity, sistently predicts the larger value. c*, is a quantity which reflects the effective energy level of the propellants and subsonic The discrepancies in the values of thrust expansion. Values for the characteristic velocity decrement predictions translate directly to dis- as predicted by both procedures are tabulated in crepancies in specific impulse loss discrepancies. Table 8. The characteristic velocity values pre- The disjoint procedure predicts an Is loss of dicted by the ODE portion of both procedures are 11.0, 12.4, 13.0, and 13.6 sec from tle 60:l noz- constant for all area ratios. There is an almost zle to the 1OOO:l nozzle. This contrasts sharply negligible (0.2 percent) difference between the with the 12.7, 15.6, 16.8, and 20.2 sec losses values calculated by the two procedures, with the which the integrated procedure predicts for the disjoint procedure predicting a lower value than 60:l to 1OOO:l nozzles. the integrated procedure. Differences between the thermodynamic datahases used in the disjoint The disagreement in specific impulse at the and the integrated procedures' ODE versions can 1OOO:l area ratio result (Table 8) is surprisingly account for the difference in these predicted low, especially in light of the large thrust values. decrement discrepancy between the two procedures. The two orocedures were in qood agreement on At the boundary layer level of computations specific impulse predictions. (accounting for the area change at the throat), the difference between the computed c* values are Notes on Effects of Wall Lemperature Profile on within 0.6 percent of each other. Again, the Results integrated procedure predicted a greater value than did the disjoint procedure. In an attempt to investiqate the effect of wall temperature profile on the predictions, the The thermodynamic datahases used in the inte- 2OO:l area ratio case was rerun using the grated and disjoint procedures were different. integrated procedure with two different wall tem- This is most likely the cause of the differences perature profiles. The two new wall temperature between the two procedures. profiles were the baseline wall temperature profile displaced by *500 deqrees Rankine (referred Thrust Coefficient, Cf to as +500 "R and -500 "R wall temperature profiles, respectively). All three profiles are Tabulated values of the thrust coefficient plotted in Fig. 11. can be found in Table 8. The thrust coefficient as calculated by ODE in both procedures show very The effect of wall temperature profile on good agreement. The variation in equilibrium the momentum thickness, thrust decrement, and values between procedures is less than 0.1 percent local skin friction coefficient is small (i.e., for all area ratios. This variation is caused by less than 5 percent) for both profiles. Likewise, the thermodynamic database difference mentioned the values of vacuum specific impulse, c*, and in the previous section. CF were all within 0.17 percent of the baseline calculations for both wall temperature profiles. In all cases, the integrated procedure con- The displacement thickness predicted by the inte- sistently predicts a slightly higher CF value. grated procedure using the +500 "R wall tempera- The thrust coefficient for the two different pro- ture profile is 14.8 percent qreater and the cedures differs by 4.7, 3.8, 3.2, and 2.4 percent -500 R wall temperature profile is 15.0 percent for the 60:1, 200:1, 400:1, and 1OOO:l area ratio less than the oriqinal predictions (Fig. 12). cases, respectively. The effect of the +500 R temerature orofile on heat loss rate resulted in a 7.8 percent exit This result taken with respect to the heat plane value decrease from the baseline value and loss rate results point to an overall consistency the -500R wall temperature profile resulted in a between the two procedures. The disjoint proce- 6.1 percent exit plane value increase (Fiq. 13). dure predicts a lower heat loss rate as well as a lower thrust coefficient. Based on this comparison, the prediction by the inteqrated procedure of the momentum thick- Vacuum Specific Impulse, ISp ness, local skin friction coefficient, and thrust decrement is seen to be relatively insensitive to The vacuum specific impulse is a measure of wall temperature profile, whereas the displacement the efficiency of a rocket engine. The thrust thickness and heat loss predictions are very sen- decrement is the loss of thrust due to boundary sitive. This indicates that if the analysis being layer growth in the rocket nozzle. These two done is for nozzle design, the wall temperature quantities are discussed together because the is a very critical input. A nozzle with too great thrust decrement i s converted to an impulse decre- or too small of a potential wall displacement will ment and subtracted from the ideal value of Isp result in different exit pressures, Mach numbers, predicted prior to the boundary layer analysis. and wall angles than those desired. However, if

4 the analysis is to determine specific impulse or oletion of an analysis of one rocket nozzle for skin friction of an already fabricated nozzle, an the disjoint procedure required considerably more approximate temperature profile can be used to clock time than did one run for the integrated yield satisfactory results. procedure. This was due to the manual transmission and reconditioning of data from the output Concludinq Remarks of one computer program to the input of the next computer program. Moving the data between pro- An analytical study was conducted which com- grams in the disjoint procedure was done as care- pared the outputs from two different procedures, fully as possible and it was assumed that no both of which followed the standard JANNAF meth- error was introduced because of incorrect data odology of predicting liquid rocket engine entry. However, this resulted in increasing the performance. The predicted values by both proce- complexity of the analysis and prolonged the dures of characteristic velocity and thrust amount of time required to do an entire perform- coefficient are within 0.6 and 3.0 percent of ance prediction analysis. Automated interfacinq each other, respectively. Predicted vacuum speci- between programs was a major step forward with fic impulse values are withir, 1.3 percent of each the introduction of TDK.85 (i.e., the integrated other. Comparing these parameters alone, the two procedure). The inteqrated process eliminated procedures displayed good agreement between this possible source of error and also reduced themselves. the total time required for a thorouqh analysis. However, the procedures' predictions of dis- References placement thickness and skin friction coefficient were within a maximum difference of approximately 1. "JANNAF Rocket Engine Performance Prediction 10 percent, momentum thicknesses were within and Evaluation Manual," CPIA-PUBL-245, Chemi- 20 percent, heat loss rates were within ....cal Propulsion. Information Agency, Laurel, 30 perc~iit,arid thi-usi loss due tu buuriridry layer I~J,Apr. 1~13. growth was within 40 percent. This was due to the differences between the two procedures' input 2. Evans, R.M., "Boundary Layer Integral Matrix wall pressure profiles and physical models (e.g. Procedure for JANNAF, BLIMP-J User's Manual," Cebeci-Smi th eddy-viscosi ty model ). Upon inspec- Aerotherm-UM-75-64, Aerotherm Acurex Corp., tion of these parameters, agreement between the Mountain View, CA, July 1975. (NASA two procedures can be seen to be poor. Experi- CR-144046) mental test results are required to pinpoint which (if either) of the two procedures better 3. Nickerson, G.R., Coats, D.E., and Dang, L.D., models the real situation. "Two-Dimensional Kinetic Reference Computer Proqram, (TDK) ," NASA CR-178628, 1985. Therefore, if approximate values of the gross performance parameters are the object of the anal- 4. Nickerson, G.R. and Dang, L.D., Two- ysis, either procedure will produce a value within Dimensional Kinetics Computer Program for current measurement accuracy limits of the other. Orbit Transfer Vehicles," 22nd JANNAF Combus- It can also be seen, then, that if accurate axial tion Meetin Vol. 1, D.S. Eggleston, ed., profiles of the boundary layer quantities are +PIA-PUBL-432-VOL-1, Chemical Propulsion desired, the procedure used (ar even the choice Information Aqency, Laurel, MD, 1985. of boundary layer modules) will greatly affect the result. The disjoint procedure predicts 5. Gordon, S. and McBride, R.J., Computer Pro- greater values of displacement thickness, and qram for Calculation of Complex Chemical momentum thickness, and lower values of skin fric- Equilibrium Compositions, Rocket Performance, tion coefficient, thrust decrement, and heat loss Incident and Reflected Shocks, and Chapman- rate profiles, as compared to the inteqrated Jouguet Detonations,'' NASA SP-273, 1976. procedure. 6. Bittker, A. and Scullin, V.J., 'I General Effect of wall temperature profile on repor- Chemical Kinetics Computer Program for Static ted parameters was investigated by displacing the and Flow Reactions, with Application to Com- baseline wall temperature profile by a500 "R. bustion and Shock-Tube Kinetics,'' NASA Less than f0.2 percent change was experienced by TN D-6586, 1972. values of characteristic velocity, thrust coefficient, vacuum specific impulse, and skin friction 7. Huzel, D.K. and Huang, D.H., "Design of Liq- coefficient. Parameters which showed less than uid Propellant Rocket Engines," 2nd ed., NASA '5 percent change included momentum thickness and SP-125, 1971. thrust decrement. Greatly affected by the change in wall temperature profile were boundary layer 8. Rao. G.V.R.. "Exhaust Nozzle Contour for displacement thickness (changed by 15 percent) Optimum Thrust," Jet Propulsion, Vol. 28, and heat loss rate (which displayed a *7 percent No. 6, June 1958, op. 311-382. change). Other areas of concern deal with the opera- tion of the computer programs themselves. Com-

5 APPENDIX A

INVISCID CONTOUqS

I E = 60:l E = ZOO:] E = 400:l E = 1OOO:l

RY 2, RY ZY R, ZY RY 2, in. in. in. in. in. in. in. in.

0.50000 0.00000 I. 50000 0.00000 3.50300 0.00000 0.50000 0.00000 .52980 .lo597 .55153 .13874 .55388 .13949 .55639 .14022 .56325 .16766 .59457 .20374 .60268 .20635 .61461 .20968 .59797 .22951 .63923 .26926 .65319 .27376 .67446 .27976 .63416 .29209 .68588 .33600 .70587 .34248 .73637 .35120 .67215 .35607 .73490 .40467 .76129 .4 1340 .80116 .42507 .71218 .42222 .78640 .47662 .81966 .48771 .87004 .50288 .75426 .49182 ,84161 .55344 .88227 .56736 .94477 .58677 .79958 .56659 .90207 .63747 .95098 .65477 1.0277 .6793 1 .84938 .64881 .96987 .73163 1.0283 .75311 1.1196 .78382 .90556 .74142 1.0459 .83929 1.1155 .86613 1.2243 .90482 .96802 .84720 1.1331 .96480 1.2160 .99859 1.3461 1.0477 1.0390 .97000 1.2343 1.1129 1.3331 1.1558 1.4883 1.2185 1.1210 1.1142 1.3497 1.2880 1.4679 1.3429 1.6536 1.4235 1.2121 1.2820 1.4821 1.4949 1.6232 1.5652 1.8453 1.6690 1.3150 1.4776 1.6303 1.7361 1.7988 1.8263 2.0638 1.9598 1.4255 1.6998 1.7915 2.0114 1.9917 2.1265 2.3063 2.2972 1.5447 1.9494 1.9648 2.3201 2.1993 2.4644 2.5693 2.6798 1.6673 2.2218 2.1468 2.6604 2.4194 2.8396 2.8505 3.1077 1.7947 2.5208 2.3386 3.0379 2.6539 3.2588 3.1532 3.5903 2.0089 3.0658 2.6997 3.8075 3.1041 4.1248 3.7441 4.6011 2.1994 3.6005 3.0833 4.7110 3.5887 5.1512 4.3913 5.8145 2.4603 4.4208 3.4157 5.5728 4.0157 6.1401 4.9708 6.9967 2.6743 5.1883 3.8634 6.8626 4.6000 7.6336 5.7804 8.8049 2.9330 6.2492 4.3107 8.3208 5.1980 9.3425 6.6255 10.898 3.1450 7.2652 4.6689 9.6290 5.6854 10.888 7.3290 12.812 3.3071 8.1523 5.0843 11.333 6.2638 12.919 8.1803 15.351 3.5316 9.6024 5.4424 12.994 6.7733 14.915 8.9475 17.870 3.7040 10.965 5.9134 15.518 7.4628 17.977 10.013 21.772 3.8729 12.641 6.4260 18.868 8.2451 22.086 11.267 27.075 6.8083 21.976 8.8592 25.944 12.295 32.116 7.0711 24.576 9.3302 29.418 13.116 36.702 14.326 44.635 15.811 57.196

6 TABLE 1. - INPUTS REQUIRED FOR THE DISJOINT PROCEDURE

Program Inwts From

Chamber pressure Specified Mixture ratio Area ratlo Fuel and oxydizer enthalpies I Mole fractions at throat ODE Throat temperature Throat velocity Pressure at throat i Contour points Spec if ied Throat area Chamber pressure

BLIMP Wall temperature profile waii pressure profile ODKI Wall contour points Spec ified Throat radlus Spec if ied 1Chamber pressure Spec if Ied Options used in BLIMP program: Nodal refit on. Cebeci-Smlth turbulence model. Buddenberg-Wilke mixture formula for viscosity. Mason-Saxena with Eucken correction for thermal conductivity.

Program Inputs From

TDK.83 Contraction ratio Spec1 f ied Radius of throat Upstream throat radius of curvature Downstream throat radius of curvature Wall angle of convergent section Radius of curvature into convergent section Nozzle exit angle End-of-circle angle Wall contour points Area ratio Chamber pressure Mixture ratio 1 TABLE 3. - LIST OF CHEMICAL REACTIONS AND THREE-BODY RECOMBINAlION-OISSOCIATION REACT IONS

(a) Chemical reactions

H f02 =OH +O 0 +H2 =OH tH H2 t OH = H20 t H Area ratio 60:l 200:l 400:l 1OOO:i OH t OH = 0 t H20 H t 02 = H02 t M Radius (in.) 3.87 7.07 10.00 15.81 0 to = 02 Length (in.) 12.64 24.58 35.51 57.20 H +H =H2 11 H t OH = H20 t H2 t H02 = H20 t OH M t H202 = 20H H2 t 02 = 20H H t H02 = OH t OH 0 t H02 = OH t 02 OH t H02 = H20 t 02 2H20 = H202 t 02 OH t H202 = H20 t H02 0 + H202 = OH t H02 H t H202 = H20 t OH

(b) Three-body recombination- dissoc iati on reactions

H t 02 = H20 t M H tH =H2 tM M + H202 = 20H H t OH = H20 t M

TABLE 5. - LIST OF ROCKET ENGINE GEOMElRY PARAMETERS

ECRAl = Contraction ratio of combustlon chamber = 4.223 RWIU = Upstream throat radius of curvature = 2.0 RWlD = Downstream throat radius of curvature = 0.4 RI Normalized inlet wall radius = 1E-4 EPS - Nozzle expansion ratio (see table for values) THETA = Nozzle attachment angle (see table for values) THETAI = Nozzle inlet angle (see table for values) THE Nozzle exit angle (see table for values)

Area ratio

8 Procedure 60:l 2OO:l 400:l 1OOO:l

BLIMP 38 40 40 40 TOK 43 8 8 11

TOK 100/3 100/5 200/5 200/5 1 I I I I I

TABLE 7. - EXIT PLANE VALUES OF BOUNDARY LAYER PARAMETERS

[Entries are disjoint/integrated procedure values. Numbers in parentheses are (t500 "R/-500 OR) wall temperature profile values usjng integrated procedure.]

I Area ratios

60: 1 2OO:l 400:l 1OOO:l

thickness (ft) 0.00448/0.00455 0 .01755/0.01587 0.03560/0.02551 0.08701 /O. 06409 ( .01822/.01 348)

Moment um thickness (ft) .00430/.00385 .00851/.00764 .00851/.01054 .02045/.017bO ( .00737/.00774)

Thrust decrement (lbf) 36.76/42.03 41.21/51 .74 43.29/55.74 45.43/66.96 (49.38/53.04)

Skin friction coefficient .0031 b/.00338 .00294/ .00304 .00279/.0031 1 .00270/.00274 (.00303/.00304)

Heat loss rate (BTWsec) 592.b/b96.0 631 .4/789.0 655.1/847.5 678.7/921.4 (727.7/837.0)

9 TABLE 8. - PERFORMANCE COMPARISON

[Constants: g = 32.1739 ft/sec/sec; pc = 1000 psIa; At = 0.00545415 ft2.]

(a) The disjoint procedure

C*( EL) ft/sec

7576.41 200:l 400:l 1OOO:l 1 (b) The Integrated procedure

C*( ODE) C*(BL) CF(ODE) cF(BL) CF(BL) ratio ft/sec ft/sec t500 OR -500 OR

7590 7622.57 1.878 1.8723 200 :1 1.978 1.9313 1.9299 1.9346 400:l 2.021 1.9561 1OOO:l I 1 2.065 1.9694 (c) The dlsjoint procedure

dT, dIsp ratio lbf s ec

36.76 11.02 444.4 41.21 12.35 459.9 485.3 43.29 12.98 466.4 45.43 13.62 472.7

(d) The integrated procedure t--- 60:l 461 .O 42.026 12.68 443.95 2OO:l 479.0 51.735 15.60 457.55 457.06 458.16 400: 1 486.5 55.745 16.82 463.44 1OOO:l 494.2 66.959 20.20 466.60

10 INPUTS PROGRAM OUTPUTS

CHAMBER PRESSURE MIXTURE RATIO THROAT MOLE FRACTIONS AREA RATIO ODE THROAT TEMPERATURE e = THETA - THROAT VELOCITY FUEL AND OXIDIZER ei = THETA I ENTHALPIES THROAT PRESSURE ee = THE * I

THROAT AREA I NOZZLE WALL CONTOUR ODK t-/ WALL PRESSURE PROFIL -1 SPECIFIC IMPULSE I THRUST COEFFICIENT CHARACTERISTIC VELOCITY DISPLACEMENT THICKNESS WALL TEMPERATURE PROFILE -D BLIMP MOMENTUM THICKNESS HEAT LOSS RATE LOCAL SKIN FRICTION . COEFF!C!ENT!-!FFF!!-!FNT I 1 I FIGURE 1. - DISJOINT PROCEDURE FLOW DIAGRAM. FIGURE 2. - VARIABLES WHICH DESCRIBE NOZZLE GEOMETRY.

2500 - PROFILE - BASELINE 1750 - --- RL-10 2000 -,I ---e----- SSME PI O 1500 - W ’\

FIGURE 3. - BASELINE WALL TEMPERATURE PROFILE FOR FIGURE 4. - COMPARISON OF BASELINE, RL10, AND SSME 1OOO:l AREA RATIO NOZZLE. WALL TEMPERATURE PROFILES FOR THE 200:l NOZZLE.

11 L PROCEDURE 10 c PROCEDURE ,020 DISJOINT - L u 5 -08 L ------INTEGRATED / . .016 w v) r v) VY rW ;.06 y .012 c u cI rcac .04 uY 4 .02 2 n 0 1 2 3 4 5 0 AXIAL DISTANCE. FT AXIAL DISTANCE. FT FIGURE 5. - COMPARISON OF BOUNDARY LAYER DISPLACEMENT FIGURE 6. - CMPARISON OF BOUNDARY LAYER MOMENTUM THICK- THICKNESS, NOZZLE AREA RATIO = 1OOO:l. NESS, NOZZLE AREA RATIO = 1OOO:l.

PROCEDURE PROCEDURE 8o r - DISJOINT eoo8r ------INTEGRATED u 60 P;

I 0 1 2 3 4 5 0 1 2 3 4 5 AXIAL DISTANCE, FT AXIAL DISTANCE. FT FIGURE 7. - COMPARISON OF LOCAL SKIN FRICTION COEFFICIENT FIGURE 8. - COMPARISON OF THRUST DECREMENT DUE TO BOUND- NOZZLE AREA RATIO = 1OOO:l. ARY LAYER GROWTH, NOZZLE AREA RATIO = 1OOO:l.

12 PROCEDURE INTEGRATED. EQUILIBRIUM I,, --€I---DISJOINT. EQUILIBRIUM. I,, PROCEDURE --om-DISJOINT. BL I,, PERFORMANCE * INTEGRATED. BL I,, PERFORMANCE 1000 L- DISJOINT

E 800 \YI 3 A5 V; 600 v) 0A k 4 460 + Vw !.& !.& 400 a 450

200 440 0 1 2 3 4 5 200 400 600 800 1000 AXIAL DISTANCE, FT AREA RATIO FIGURE 9. - COMPARISON OF HEAT LOSS TO THE WALL, NOZZLE FIGURE 10. - COMPARISON OF INTEGRATED AND DISJOINT PRO- AREA RATIO = 1OOO:l. CEDURES I,, PREDICTIONS.

WALL TEMPERATURE PROFILES BASELINE + 500 OR BASELINE BASELINE - 500 OR

2000 0" 0" 1 - 1500 wE

4z e 1000 2 500 3

AXIAL DISTANCE. IN. FIGURE 11. - COMPARISON OF BASELINE WALL TEMPERATURE PROFILE. BASELINE + 500 OR, AND BASELINE - 500 OR.

13 WALL TEMPERATURE .02 - PROFILES t ------BASELINE + 500 OR 6 ,016 - BASELINE !& --- BASELINE - 500 OR E .012 - z c

0 .5 1.0 1.5 2.0 AXIAL DISTANCE, FT FIGURE 12. - COMPARISON OF BOUNDARY LAYER DISPLACE- MENT THICKNESS BETWEEN BASELINE, + 500 OR. AND - 500 OR WALL TEMPERATURE PROFILES.

WALL TEMPERATURE PROFILES BASELINE + 500 OR BASEL I NE --- BASELINE - 500 OR

v) 5 600 w4c 500

0 .4 .8 1.2 1.0 2.0 AXIAL POSITION. FT FIGURE 13. - COMPARISON OF HEAT LOSS RATE TO THE WALL BETWEEN BASELINE, + 500 OR, AND - 500 OR WALL TEMPERA- , TURE PROFILES .

14 1. Report No. NASA TM-89814 2. Government Accession No. 3. Recipient's Catalog No. AIAA-87- 207 1 4. Title and Subtitle 5. Report Date

Comparison of Two Procedures for Predicting Rocket - Engine Nozzle Performance 6. Performing Organization Code 506-42-21

7. Author(s) 8. Performing Organization Report No. Kenneth J. Davidian E-3458

10. Work Unit No.

~~ I 9. Performing Organization Name and Address 11. Contract or Grant No. National Aeronautics and Space Administration r Lewis Research Center Cleveland, Ohio 44135 13. Type of Report and Period Covered 2. Sponsoring Agency Name and Address 1 Technical Memorandum

National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D.C. 20546

I 5. Supplementary Notes < Prepared for the 23rd Joint Propulsion Conference, cosponsored by the AIAA, SAL, ASME, and ASLt, San Diego, California, June 29 - July 2, 1987.

6 Abstract lwo nozrle performance prediction procedures which are based on the standardized JANNAF methodology are presented and compared for four rocket engine nozrles. lhe first procedure required operator intercedence to transfer data between the individual performance programs. The second procedure is more automated in that all necessary programs are collected into a single computer code, thereby eliminating the need for data reformatting. Results from both procedures show similar trends but quantitative differences. Agreement was best in the predictions of specific impulse and local skin friction coefficient. Other compared quantities include characteri5tic velocity, thrust coefficient, thrust decrement, boundary layer displacement thickness, momentum thickness, and heat loss rate to the wall. Effects of wall temperature profile used as an input to the programs was inVeStigdted by running three wall temperature profiles. It was found that this change greatly affected the boundary layer displacement thickness and heat loss to the wall. The other quantities, however, were not drastically affected by the wall temperature profile change.

17. Key Words (Suggested by Author@)) 18. Distribution Statement Chemical kinetics; Rocket engine; Unclassified - unlimited Nozrle; Performance prediction; STAR Category 20 Boundary layer

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 22. Price' Unclassified Unclassified 15 A02

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